Title: N_p conditions for curves in weighted projective space

 

Abstract: Say we have a closed embedding of a smooth curve C into projective space, and let \(R\) be its homogeneous coordinate ring. A famous theorem of Green gives a tight relationship between a certain geometric property of the embedding (namely the degree of the line bundle inducing it) and a certain homological property of R (the linearity of its free resolution over the coordinate ring of projective space). The goal of this project is to generalize this result to curves in weighted projective space.

 

This is joint work with Daniel Erman.